Excuse me, over-read that; anyway, then you double it
In[43]:= Select[Subsets[Subsets[{x1, x2, x3, x4}, {2}], {2}], Sort[Flatten[#]] == {x1, x2, x3, x4} &]
Out[43]= {{{x1, x2}, {x3, x4}}, {{x1, x3}, {x2, x4}}, {{x1, x4}, {x2, x3}}}
it's not efficient because the nested Subset call generates far more expressions than needed: Select has to trim that back
In[42]:= Select[
Subsets[Subsets[{x1, x2, x3, x4, x5, x6, x7, x8}, {2}], {4}],
Sort[Flatten[#]] == {x1, x2, x3, x4, x5, x6, x7, x8} &]
Out[42]= {{{x1, x2}, {x3, x4}, {x5, x6}, {x7, x8}}, {{x1, x2}, {x3, x4}, {x5, x7}, {x6, x8}}, {{x1, x2}, {x3, x4}, {x5, x8}, {x6, x7}},
{{x1, x2}, {x3, x5}, {x4, x6}, {x7, x8}}, {{x1, x2}, {x3, x5}, {x4, x7}, {x6, x8}}, {{x1, x2}, {x3, x5}, {x4, x8}, {x6, x7}},
{{x1, x2}, {x3, x6}, {x4, x5}, {x7, x8}}, {{x1, x2}, {x3, x6}, {x4, x7}, {x5, x8}}, {{x1, x2}, {x3, x6}, {x4, x8}, {x5, x7}},
{{x1, x2}, {x3, x7}, {x4, x5}, {x6, x8}}, {{x1, x2}, {x3, x7}, {x4, x6}, {x5, x8}}, {{x1, x2}, {x3, x7}, {x4, x8}, {x5, x6}},
{{x1, x2}, {x3, x8}, {x4, x5}, {x6, x7}}, {{x1, x2}, {x3, x8}, {x4, x6}, {x5, x7}}, {{x1, x2}, {x3, x8}, {x4, x7}, {x5, x6}},
{{x1, x3}, {x2, x4}, {x5, x6}, {x7, x8}}, {{x1, x3}, {x2, x4}, {x5, x7}, {x6, x8}}, {{x1, x3}, {x2, x4}, {x5, x8}, {x6, x7}},
{{x1, x3}, {x2, x5}, {x4, x6}, {x7, x8}}, {{x1, x3}, {x2, x5}, {x4, x7}, {x6, x8}}, {{x1, x3}, {x2, x5}, {x4, x8}, {x6, x7}},
{{x1, x3}, {x2, x6}, {x4, x5}, {x7, x8}}, {{x1, x3}, {x2, x6}, {x4, x7}, {x5, x8}}, {{x1, x3}, {x2, x6}, {x4, x8}, {x5, x7}},
{{x1, x3}, {x2, x7}, {x4, x5}, {x6, x8}}, {{x1, x3}, {x2, x7}, {x4, x6}, {x5, x8}}, {{x1, x3}, {x2, x7}, {x4, x8}, {x5, x6}},
{{x1, x3}, {x2, x8}, {x4, x5}, {x6, x7}}, {{x1, x3}, {x2, x8}, {x4, x6}, {x5, x7}}, {{x1, x3}, {x2, x8}, {x4, x7}, {x5, x6}},
{{x1, x4}, {x2, x3}, {x5, x6}, {x7, x8}}, {{x1, x4}, {x2, x3}, {x5, x7}, {x6, x8}}, {{x1, x4}, {x2, x3}, {x5, x8}, {x6, x7}},
{{x1, x4}, {x2, x5}, {x3, x6}, {x7, x8}}, {{x1, x4}, {x2, x5}, {x3, x7}, {x6, x8}}, {{x1, x4}, {x2, x5}, {x3, x8}, {x6, x7}},
{{x1, x4}, {x2, x6}, {x3, x5}, {x7, x8}}, {{x1, x4}, {x2, x6}, {x3, x7}, {x5, x8}}, {{x1, x4}, {x2, x6}, {x3, x8}, {x5, x7}},
{{x1, x4}, {x2, x7}, {x3, x5}, {x6, x8}}, {{x1, x4}, {x2, x7}, {x3, x6}, {x5, x8}}, {{x1, x4}, {x2, x7}, {x3, x8}, {x5, x6}},
{{x1, x4}, {x2, x8}, {x3, x5}, {x6, x7}}, {{x1, x4}, {x2, x8}, {x3, x6}, {x5, x7}}, {{x1, x4}, {x2, x8}, {x3, x7}, {x5, x6}},
{{x1, x5}, {x2, x3}, {x4, x6}, {x7, x8}}, {{x1, x5}, {x2, x3}, {x4, x7}, {x6, x8}}, {{x1, x5}, {x2, x3}, {x4, x8}, {x6, x7}},
{{x1, x5}, {x2, x4}, {x3, x6}, {x7, x8}}, {{x1, x5}, {x2, x4}, {x3, x7}, {x6, x8}}, {{x1, x5}, {x2, x4}, {x3, x8}, {x6, x7}},
{{x1, x5}, {x2, x6}, {x3, x4}, {x7, x8}}, {{x1, x5}, {x2, x6}, {x3, x7}, {x4, x8}}, {{x1, x5}, {x2, x6}, {x3, x8}, {x4, x7}},
{{x1, x5}, {x2, x7}, {x3, x4}, {x6, x8}}, {{x1, x5}, {x2, x7}, {x3, x6}, {x4, x8}}, {{x1, x5}, {x2, x7}, {x3, x8}, {x4, x6}},
{{x1, x5}, {x2, x8}, {x3, x4}, {x6, x7}}, {{x1, x5}, {x2, x8}, {x3, x6}, {x4, x7}}, {{x1, x5}, {x2, x8}, {x3, x7}, {x4, x6}},
{{x1, x6}, {x2, x3}, {x4, x5}, {x7, x8}}, {{x1, x6}, {x2, x3}, {x4, x7}, {x5, x8}}, {{x1, x6}, {x2, x3}, {x4, x8}, {x5, x7}},
{{x1, x6}, {x2, x4}, {x3, x5}, {x7, x8}}, {{x1, x6}, {x2, x4}, {x3, x7}, {x5, x8}}, {{x1, x6}, {x2, x4}, {x3, x8}, {x5, x7}},
{{x1, x6}, {x2, x5}, {x3, x4}, {x7, x8}}, {{x1, x6}, {x2, x5}, {x3, x7}, {x4, x8}}, {{x1, x6}, {x2, x5}, {x3, x8}, {x4, x7}},
{{x1, x6}, {x2, x7}, {x3, x4}, {x5, x8}}, {{x1, x6}, {x2, x7}, {x3, x5}, {x4, x8}}, {{x1, x6}, {x2, x7}, {x3, x8}, {x4, x5}},
{{x1, x6}, {x2, x8}, {x3, x4}, {x5, x7}}, {{x1, x6}, {x2, x8}, {x3, x5}, {x4, x7}}, {{x1, x6}, {x2, x8}, {x3, x7}, {x4, x5}},
{{x1, x7}, {x2, x3}, {x4, x5}, {x6, x8}}, {{x1, x7}, {x2, x3}, {x4, x6}, {x5, x8}}, {{x1, x7}, {x2, x3}, {x4, x8}, {x5, x6}},
{{x1, x7}, {x2, x4}, {x3, x5}, {x6, x8}}, {{x1, x7}, {x2, x4}, {x3, x6}, {x5, x8}}, {{x1, x7}, {x2, x4}, {x3, x8}, {x5, x6}},
{{x1, x7}, {x2, x5}, {x3, x4}, {x6, x8}}, {{x1, x7}, {x2, x5}, {x3, x6}, {x4, x8}}, {{x1, x7}, {x2, x5}, {x3, x8}, {x4, x6}},
{{x1, x7}, {x2, x6}, {x3, x4}, {x5, x8}}, {{x1, x7}, {x2, x6}, {x3, x5}, {x4, x8}}, {{x1, x7}, {x2, x6}, {x3, x8}, {x4, x5}},
{{x1, x7}, {x2, x8}, {x3, x4}, {x5, x6}}, {{x1, x7}, {x2, x8}, {x3, x5}, {x4, x6}}, {{x1, x7}, {x2, x8}, {x3, x6}, {x4, x5}},
{{x1, x8}, {x2, x3}, {x4, x5}, {x6, x7}}, {{x1, x8}, {x2, x3}, {x4, x6}, {x5, x7}}, {{x1, x8}, {x2, x3}, {x4, x7}, {x5, x6}},
{{x1, x8}, {x2, x4}, {x3, x5}, {x6, x7}}, {{x1, x8}, {x2, x4}, {x3, x6}, {x5, x7}}, {{x1, x8}, {x2, x4}, {x3, x7}, {x5, x6}},
{{x1, x8}, {x2, x5}, {x3, x4}, {x6, x7}}, {{x1, x8}, {x2, x5}, {x3, x6}, {x4, x7}}, {{x1, x8}, {x2, x5}, {x3, x7}, {x4, x6}},
{{x1, x8}, {x2, x6}, {x3, x4}, {x5, x7}}, {{x1, x8}, {x2, x6}, {x3, x5}, {x4, x7}}, {{x1, x8}, {x2, x6}, {x3, x7}, {x4, x5}},
{{x1, x8}, {x2, x7}, {x3, x4}, {x5, x6}}, {{x1, x8}, {x2, x7}, {x3, x5}, {x4, x6}}, {{x1, x8}, {x2, x7}, {x3, x6}, {x4, x5}}}